Solution of Exercise 1: ER-Diagrams
Due: November 5, Ross closing time
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Print out this exercise and answer the questions on the printout. For Problem 4 you should attach
extra pages, as needed. Remember to register for the course so that your exercise may be graded.
Problem 2 (35 points)
Below we present several entity relationship diagrams for modeling information about authors, editors
and books. Note that aid is the key of Authors, eid is the key of Editors and bid is the key of Books.
For each of the entity relationship diagrams below:
(a) State briefly the meaning of the diagram. Emphasize the constraints in the diagrams.
(b) Suppose that there are 300 authors, 1000 books and 10 editors. What is the maximal number of
triples that R contains?
(c) Suppose that there are 300 authors, 1000 books and 10 editors. What is the minimal number of
triples that R contains?
Editors
R
eid
Books
bid
aid
Authors
(1a) Meaning: The diagram models information about the editing of books written by authors. Each
editor edits any number of books and works with any number of authors. Each book is written by
any number of authors and is edited by any number of editors. Each author writes any number of
books and works with any number of editors.
(1b) Maximal number of triples: 3000000
(1c) Minimal number of triples: 0
1
Editors
R
eid
Books
bid
aid
Authors
(2a) Meaning: Each editor edits any number of books and works with any number of authors. Each
book is written by any number of authors and is edited by any number of editors. Each author
writes at most one book and works with at most one editor.
(2b) Maximal number of triples: 300
(2c) Minimal number of triples: 0
Editors
R
eid
Books
bid
aid
Authors
(3a) Meaning: Each editor edits at most one book and works with at most one author. Each book is
written by any number of authors and is edited by any number of editors. Each author writes at
most one book and works with at most one editor.
(3b) Maximal number of triples: 10
(3c) Minimal number of triples: 0
Editors
R
eid
Books
bid
aid
Authors
(4a) Meaning: Each editor edits at least one book and works with at least one author. Each book is
written by any number of authors and is edited by any number of editors. Each author writes
exactly one book and works with exactly one editor.
(4b) Maximal number of triples: 300
(4c) Minimal number of triples: 300
Editors
R
eid
Books
bid
aid
Authors
2
(5a) Meaning: Each editor edits at least one book and works with at least one author. Each book is
written by at least one author and is edited by at least one editor. Each author writes at least one
book and works with at least one editor.
(5b) Maximal number of triples: 3000000
(5c) Minimal number of triples: 1000
Problem 3 (25 Points)
1. As in Problem 2, we consider information about Authors, Books and Editors. We wish to store
information about which author wrote which book with which editor. Two basic approaches can
be taken to model this information:
Editors
Edits
Books
eid
bid
Writes
Contact
Editors
R
eid
Books
Authors
bid
aid
aid
Authors
(a)
(b)
(a) Assuming that there are no further constraints on the information, which of the two diagrams
presented are more suitable for modeling the information? Can the information be captured
in both diagrams? Explain.
Diagram (a) clearly captures the required information since the relationship “R” stores information about triples of books, authors and editors such that an author writes a book with an
editor. Diagram (b) also captures the required information. For example,
• if editors e1 and e2 both edit book b1
• if author a1 writes book b1
• if author a1 works with editor e1 and e2
we can infer that b1 is written by a1 and edited by e1 . We can also infer that b1 is written by
a1 and edited by e2 .
Note: suppose that the relation between “Editor” and “Books” is “Can Edit”,
• if editors e1 and e2 both can edit book b1
3
• if author a1 writes book b1
• if author a1 works with editor e1 and e2
we are not able to infer from this if b1 , written by a1 , is edited by e1 or by e2 .
Thus, in this case, the information cannot be captured in both diagrams.
(b) Suppose that each book is edited by at most one editor. Can you add edge constraints (arrows)
to the diagram on the left in order to capture this information? What about the diagram on
right? Explain.
We cannot add an edge to diagram (a) to capture this information. If we add an arrow from
“Books” to “R” then this implies that each book is edited by at most one editor and written
by at most one author, which is not part of the assumption. On the diagram (b), we can add
an arrow from “Books” to “Edits”, to correctly capture the information.
2. What is wrong with using the following diagram to model the information?
Writes
Authors
aid
Books
bid
eid
This diagram implies that each book written by an author, is edited by at most one editor. This is
because a given pair of author and book can participate at most once in the relationship “Writes”.
Problem 4 (40 Points)
Congratulations! You have gotten a job planning databases for the European Union. Your first on job
assignment is to help the various countries maintain information about their inhabitants. Your model
should capture the following information:
• In each country, there are provinces, which contain towns. There cannot be two provinces with the
same name in a single country. Similarly, there cannot be two towns with the same name in a single
province.
• People live in towns. Men and women work in a town. Children learn in a school in a town.
• A person can be a man, a woman, or a child, and has a first-name, last-name, id, and birthday.
Children are any people under the age of 18.
• A man can be married to a woman (polygamy is not allowed, i.e., one man can be married only
to one woman). Although the Pope strongly disapproves, divorce, and subsequent remarriage, is
possible.
4
• For each marriage, store the date of the marriage and information about who are the children of
the married couple. You should assume that the parents of a child were married at the time of his
birth.
Draw an entity relationship diagram to model the information described above. Remember to put
edge constraints (arrows) and participation constraints (thick lines) where needed. Underline the key
attributes of each entity in the diagram. If you use the ISA relationship, state any covering and overlap
constraints that hold. Make any necessary and logical assumptions. State any such assumptions clearly.
If there are any constraints in the problem that could not be expressed in the diagram, state these clearly.
Here is a possible solution. In our solution, the assumption that “divorce, and subsequent remarriage,
is possible”, is not captured. Woman and Man cover adult and do not overlap. Same for Adult and
Child. Each child is a son of exactly one pair of parents and learns in exactly one town.There is at least
one province in each country and at least one town in each province.
country
name
firstname
in
birthday
lastname
id
province
name
people
live
in
ISA
work
town
name
adult
ISA
child
Child of
learn
date
man
Married to
5
woman